The first time I ended a lesson asking students for written work, I really wasn't thinking about the possible language difficulties of some students in the class. I didn't realize that students may have serious difficulties writing, and some may actually not write anything at all if they are left to do the task on their own.

A good way of dealing with this without eliminating the closure entirely, is to pair up students with language difficulties with others that don't have english problems. I would ask that they work together and submit one work with both their names on it. I would make sure that ELLs actually participate in the elaboration of the paragraphs by contributing their ideas, and the other student do the writing.

Allow the students about 5 minutes to discuss the problem. I inform them that what is being sought is an inequality representing the problem, along with its graph. Allow them to use graph paper, their calculator, or the desmos.com calculator if they have access.

Once finished, I call on someone and ask…. “ok, how did you and your partner develop your ideas, and what inequality did you come up with?”

They should have concluded with something like 0.25x + 0.50y ≤ 5. Ask other students if they came up with something different.

A “sometimes” error:

Be on the lookout for students who forget we are dealing with money and write the equation as:

25x + 50y ≤ 5

I then open desmos.com and ask the student to come up and graph the inequality on the screen for all to see. Ask the following questions while the graph is up:

Where are the solutions to our “pencil-pen” problem? (Students should indicate that the solutions are in the triangular region constrained by the line and both axes)

Are all the points in this triangular region a solutions to our problem? (If students have not said this already, they should indicate that only those whole number coordinates in this region are solutions, because one cannot buy fractions of pens or pencils)

After the work and the desmos demonstation, or any video demonstration for that matter, I like to ask the students to stand and stretch a bit….get blood circulating ….and then I tell them to take a few moments to think about how they can literally summarize the objective of this lesson in a paragraph of no more than three sentences. I ask each student to write their paragraph on a piece of paper. Once they’ve done so, I ask a few students to share what they wrote. I like to write a good paragraph on the board for all to copy into their notebooks.

I proceed to end the lesson using the 6 question resource (Closing _6Questions.docx). I like to do this orally. Most get this pretty well by now, and you will most certainly get a choir of correct answers.

Resources (1)

Resources

Suppose you have another pen and pencil problem. The prices, 25 cents for pencils and 50 cents for pens, and the budget, 5 bucks, remain the same. Yet you must purchase at least 3 pencils and at least 2 pens. Graph this scenario on a coordinate plane.

You should develop three inequalities, including our original .25x +.50y ≤ 5